Varying shadows with object thickness
You can use volume shaders to achieve a shadow that varies with the thickness.

I used the light path 'is shadow ray' to 'disable' the shadows of the glass shader, and to set to 0 the density of the volume inside the glass, although this is actually not necessary.



The thickest part of the model is 1 BU (1 meter).

Bear in mind that this is not realistic.